If we see a trend, the time series is not stationary (i.e. does not depend on the time of the observation).
\[ R_i = \frac{X_i - X_{i-7}}{X_{i-7}} * 100 \] \(R_i\) is the relative weekly change (increase or decrease) in percentage.
Examine the suitability for each time series \(R_i\) separately:
Explain your choice of threshold and briefly comment on the diagnostic plots for each model:
The selected threshold \(u\) is 125.
The selected threshold \(u\) is 35.
The selected threshold \(u\) is 100.
The selected threshold \(u\) is 30.
The selected threshold \(u\) is 25.
The selected threshold \(u\) is 200.
The selected threshold \(u\) is 50.
The selected threshold \(u\) is 700.
The selected threshold \(u\) is 100.
The selected threshold \(u\) is 100.
The selected threshold \(u\) is 70.
The selected threshold \(u\) is 60.
Suitability of POT: - Princess Margaret, United Kingdom, United States (?), Wiston Churchill do not seem to be suitable for POT because of the too few numbers of exceedances.
## 2016_Summer_Olympics Diana,_Princess_of_Wales Elizabeth_II
## quantile99 143.5829 363.1843 642.9873
## uncertainty 179.0603 492.1521 1753.4239
## George_VI Prince_Philip,_Duke_of_Edinburgh
## quantile99 520.8474 1111.279
## uncertainty 10635.0359 1579.921
## Princess_Margaret,_Countess_of_Snowdon Queen_Victoria
## quantile99 973.8326 421.7058
## uncertainty 17545.2920 544.1161
## United_Kingdom United_States Winston_Churchill World_War_I
## quantile99 79.08561 62.24281 846.2276 94.64611
## uncertainty 1784.17935 266.51113 7139.2646 77.44259
## World_War_II
## quantile99 61.75727
## uncertainty 48.12695
| 2016_Summer_Olympics | Diana,_Princess_of_Wales | Elizabeth_II | George_VI | Prince_Philip,_Duke_of_Edinburgh | Princess_Margaret,_Countess_of_Snowdon | Queen_Victoria | United_Kingdom | United_States | Winston_Churchill | World_War_I | World_War_II | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 2016_Summer_Olympics | 1.0000000 | 0.0714286 | 0.0000000 | 0.0714286 | 0.0357143 | 0.1071429 | 0.0357143 | 0.1071429 | 0.2142857 | 0.0357143 | 0.0000000 | 0.0357143 |
| Diana,_Princess_of_Wales | 0.0714286 | 1.0000000 | 0.0714286 | 0.0714286 | 0.1428571 | 0.0714286 | 0.0714286 | 0.0357143 | 0.0357143 | 0.0000000 | 0.0000000 | 0.0357143 |
| Elizabeth_II | 0.0000000 | 0.0714286 | 1.0000000 | 0.4642857 | 0.6071429 | 0.4642857 | 0.2857143 | 0.1071429 | 0.0000000 | 0.0357143 | 0.1428571 | 0.0000000 |
| George_VI | 0.0714286 | 0.0714286 | 0.4642857 | 1.0000000 | 0.5357143 | 0.5714286 | 0.3214286 | 0.0714286 | 0.0357143 | 0.0714286 | 0.1071429 | 0.0357143 |
| Prince_Philip,_Duke_of_Edinburgh | 0.0357143 | 0.1428571 | 0.6071429 | 0.5357143 | 1.0000000 | 0.5357143 | 0.2142857 | 0.0714286 | 0.0000000 | 0.0357143 | 0.1071429 | 0.0357143 |
| Princess_Margaret,_Countess_of_Snowdon | 0.1071429 | 0.0714286 | 0.4642857 | 0.5714286 | 0.5357143 | 1.0000000 | 0.2142857 | 0.0714286 | 0.0714286 | 0.0000000 | 0.1071429 | 0.0357143 |
| Queen_Victoria | 0.0357143 | 0.0714286 | 0.2857143 | 0.3214286 | 0.2142857 | 0.2142857 | 1.0000000 | 0.0357143 | 0.0000000 | 0.0000000 | 0.1071429 | 0.0000000 |
| United_Kingdom | 0.1071429 | 0.0357143 | 0.1071429 | 0.0714286 | 0.0714286 | 0.0714286 | 0.0357143 | 1.0000000 | 0.0357143 | 0.1785714 | 0.1071429 | 0.1071429 |
| United_States | 0.2142857 | 0.0357143 | 0.0000000 | 0.0357143 | 0.0000000 | 0.0714286 | 0.0000000 | 0.0357143 | 1.0000000 | 0.0714286 | 0.1785714 | 0.1785714 |
| Winston_Churchill | 0.0357143 | 0.0000000 | 0.0357143 | 0.0714286 | 0.0357143 | 0.0000000 | 0.0000000 | 0.1785714 | 0.0714286 | 1.0000000 | 0.1071429 | 0.0714286 |
| World_War_I | 0.0000000 | 0.0000000 | 0.1428571 | 0.1071429 | 0.1071429 | 0.1071429 | 0.1071429 | 0.1071429 | 0.1785714 | 0.1071429 | 1.0000000 | 0.4285714 |
| World_War_II | 0.0357143 | 0.0357143 | 0.0000000 | 0.0357143 | 0.0357143 | 0.0357143 | 0.0000000 | 0.1071429 | 0.1785714 | 0.0714286 | 0.4285714 | 1.0000000 |